Tuesday, March 10, 2015

Determining the radius if you know the segment length and the height of the arc

In the example of the segmented arch form I had to make in the previous post, the segment length (span of the bridge ) equaled 12 feet.  
For half a form, the measurement is six feet. 
The height of my bridge was three feet. 
Therefore the radius for a segment of a circle, according to the equation below, equals 7 1/2 feet
From calculating that radius, I determined where the axis was, and then cut my arc from the ply wood, and also drew my radiating lines at the same time.  

Here are some links that help explain how you go about determining the radius for a predetermined bridge span if it is going to be segmented arch. 



  1. or. . . you could extend the H line, knowing that the center of the circle is somewhere on that line. stretch a string or, better, chain from the top of the arch to a hypothetical center point. then, with that as a fixed point, swing the chain from the top of the arc to an end of the chord. if it's too short to reach, move the hypothetical center point up the H line and swing it again. if it extends beyond the end of the chord, move the point further down the H line. three or four such adjustments should give you the radius and the center of the circle.

  2. interesting idea, anonymous, except you've got the procedure wrong. If the chain is too short to reach the end of the chord, move the center point DOWN the H line—and UP the H line if it's too long.